You read it about half-way right. Smart contracts make the state less involved, but they don't eliminate its involvement in a transaction altogether, any more than regular written contracts eliminate the state from a transaction.

The state, or any actor for that matter, can fill multiple roles in a transaction. Intermediating all transactions is a bad role for any actor to be in (from every other actor's perspective), because it's one prone to rent-extraction. Any time you hand money over to a second party through a third party, humans have enshrined the logic that the third party—if it's big and powerful enough—can demand a cut of that transaction.

In all the cases I mentioned, the rent that is being extracted is a cut of all regular transactions. Sales tax / VAT is rent; credit card fees are rent; payment-processor fees are rent; and all of these are percentages. That is why states, credit card companies, and payment processors all have billion- (or trillion-)dollar budgets.

Imagine we eliminate that intermediation. Transactions flow directly between buyer to seller, with nobody able to take a percentile cut of them. No rent is extracted from the original transaction.

Now, in the case where a transaction doesn't go well, we do still want some actor to arbitrate disputes over a transaction. But, given the way legal systems work, it's entirely possible to do that arbitration after the fact. That is the whole idea of civil court, after all.

Such arbitrations usually result in the need for a recompensatory transaction (i.e. a lien); and such transactions need to be intermediated (i.e. supervised) by a third-party, since the two parties have already proven that they aren't mutually trustworthy. So there is a transaction here from which you probably can't stop rent from being extracted.

But that's okay! Disputes happen very rarely, while regular transactions happen all the time. The total cut of small-claims court, probate court, etc. fees, is way smaller than the total revenue of sales tax. The total amount paid to retain an arbitration service, is way smaller than the total amount earned by operating an escrow service. Etc.

The state is essential! It just doesn't belong between two people. It belongs waiting behind two people, acting as the exception-handler which one or both parties run to to report the transaction as having failed from their perspective. Then the state can step in. Much less work for the state; but also, much less rent to extract.